Volume 19, issue 4 (2019)

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On Lagrangian embeddings of closed nonorientable $3$–manifolds

Toru Yoshiyasu

Algebraic & Geometric Topology 19 (2019) 1619–1630

We prove that for any compact orientable connected 3–manifold with torus boundary, a concatenation of it and the direct product of the circle and the Klein bottle with an open 2–disk removed admits a Lagrangian embedding into the standard symplectic 6–space. Moreover, the minimal Maslov number of the Lagrangian embedding is equal to 1.

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Lagrangian submanifold, $h$–principle, loose Legendrian, Lagrangian cobordism, Lagrangian surgery, Maslov index
Mathematical Subject Classification 2010
Primary: 53D12
Secondary: 57N35, 57R17
Received: 4 November 2016
Revised: 23 December 2018
Accepted: 10 February 2019
Published: 16 August 2019
Toru Yoshiyasu
Center for Genomic Medicine
Graduate School of Medicine
Kyoto University